Variance Calculation Quiz: Calculating Variance (Basic Level)

1) What is the first step to find the variance of a data set?

Find the median

Find the mean

Square all data values

Find the mode

Variance measures how much data varies around the mean. To calculate it, you first need the mean (average). Example: For data {2, 4, 6}, Mean = (2 + 4 + 6) ÷ 3 = 12 ÷ 3 = 4.

Explanation

Variance measures how much data varies around the mean. To calculate it, you first need the mean (average). Example: For data {2, 4, 6}, Mean = (2 + 4 + 6) ÷ 3 = 12 ÷ 3 = 4.

2) After finding the mean, what should you do next?

Add the highest and lowest values

Subtract the mean from each value

Multiply all data values

Square the mean

The next step is to find each deviation from the mean. Example with {5, 7, 9}, Mean = 7 → Deviations = 5 - 7 = -2, 7 - 7 = 0, 9 - 7 = 2.

Explanation

The next step is to find each deviation from the mean. Example with {5, 7, 9}, Mean = 7 → Deviations = 5 - 7 = -2, 7 - 7 = 0, 9 - 7 = 2.

3) Why do we square each deviation?

To make negative deviations positive

To reduce the average

To make the mean smaller

To simplify division

Deviations can be negative or positive, and adding them gives zero. Squaring removes negatives and shows actual spread. For example, -3 and 3 both become 9 after squaring.

Explanation

Deviations can be negative or positive, and adding them gives zero. Squaring removes negatives and shows actual spread. For example, -3 and 3 both become 9 after squaring.

4) Variance can be negative.

True

False

Since deviations are squared, results can never be negative. The lowest possible variance is 0 (when all data points are identical).

Explanation

Since deviations are squared, results can never be negative. The lowest possible variance is 0 (when all data points are identical).

5) Find the population variance for data {5, 7, 9, 11}.

3

4

5

6

Mean = 8; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Sum = 20; Variance = 20 ÷ 4 = 5.

Explanation

Mean = 8; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Sum = 20; Variance = 20 ÷ 4 = 5.

6) If all values are equal, what is the variance?

0

1

Undefined

The mean value

When all values are identical, deviations are 0, so variance = 0.

Explanation

When all values are identical, deviations are 0, so variance = 0.

7) Select all correct steps for calculating population variance.

Find the mean

Find each deviation

Square each deviation

Add squared deviations

Divide by n

Population variance = Sum of squared deviations ÷ total number of data points (n).

Explanation

Population variance = Sum of squared deviations ÷ total number of data points (n).

Submit

8) Which mistake leads to variance = 0 when it shouldn’t?

Averaging raw deviations

Forgetting to find the mean

Squaring each deviation

Dividing by n

Adding raw deviations cancels positives and negatives. Always square before averaging.

Explanation

Adding raw deviations cancels positives and negatives. Always square before averaging.

9) Find the sample variance for {4, 7, 9}. Round to 2 decimals.

3.67

5

6.33

7

Mean = 6.67; Deviations = -2.67, 0.33, 2.33; Squares = 7.11, 0.11, 5.43; Sum = 12.65; Sample variance = 12.65 ÷ 2 = 6.33.

Explanation

Mean = 6.67; Deviations = -2.67, 0.33, 2.33; Squares = 7.11, 0.11, 5.43; Sum = 12.65; Sample variance = 12.65 ÷ 2 = 6.33.

10) For a sample, variance is calculated by dividing by n − 1.

True

False

Using n − 1 (Bessel’s correction) makes sample variance a better population estimate.

Explanation

Using n − 1 (Bessel’s correction) makes sample variance a better population estimate.

11) Two classes have test scores: A: {70,72,73,75} B: {60,70,80,90}. Which class has the higher variance?

Class A

Class B

Both equal

Cannot determine

Class B’s scores are spread further apart (60–90), so its variance is larger.

Explanation

Class B’s scores are spread further apart (60–90), so its variance is larger.

12) Which statements about variance are true?

Variance measures spread

Variance can be negative

Variance = sqrt(standard deviation)

Variance = 0 if all values equal

Variance is always non-negative

Variance measures spread, is always non-negative, and equals 0 only when all data points are identical.

Explanation

Variance measures spread, is always non-negative, and equals 0 only when all data points are identical.

Submit

13) Find the population variance for {0, 2, 4, 6}.

3

4

5

6

Mean = 3; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Variance = 20 ÷ 4 = 5.

Explanation

Mean = 3; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Variance = 20 ÷ 4 = 5.

14) Find the sample variance for {10, 12, 15}. Round to 2 decimals.

4.17

5.33

6.33

7

Mean = 12.33; Deviations = -2.33, -0.33, 2.67; Squares = 5.43, 0.11, 7.11; Sample variance = 12.65 ÷ 2 = 6.33.

Explanation

Mean = 12.33; Deviations = -2.33, -0.33, 2.67; Squares = 5.43, 0.11, 7.11; Sample variance = 12.65 ÷ 2 = 6.33.

15) Which of the following are correct steps to find sample variance?

Find the mean

Find each deviation

Square deviations

Add squared deviations

Divide by n − 1

Sample variance = (Sum of squared deviations) ÷ (n − 1). It adjusts for bias in small samples.

Explanation

Sample variance = (Sum of squared deviations) ÷ (n − 1). It adjusts for bias in small samples.

Submit

16) Variance is the __________ of the squared deviations.

Steps: 1. Find mean 2. Find deviations 3. Square each deviation 4. Take the average of the squared deviations.

Explanation

Steps: 1. Find mean 2. Find deviations 3. Square each deviation 4. Take the average of the squared deviations.

Submit

17) Find the population variance for {3, 4, 5}.

0.33

0.5

0.67

1

Mean = 4; Deviations = -1, 0, 1; Squares = 1, 0, 1; Population variance = (1 + 0 + 1) ÷ 3 = 0.67.

Explanation

Mean = 4; Deviations = -1, 0, 1; Squares = 1, 0, 1; Population variance = (1 + 0 + 1) ÷ 3 = 0.67.

18) For data {8, 10, 12}, the population variance is __________ (round to 2 decimals).

Mean = 10; Deviations = -2, 0, 2; Squares = 4, 0, 4; Variance = (4 + 0 + 4) ÷ 3 = 2.67.

Explanation

Mean = 10; Deviations = -2, 0, 2; Squares = 4, 0, 4; Variance = (4 + 0 + 4) ÷ 3 = 2.67.

Submit

19) For data {2, 3, 7}, a student added deviations to get 0 and said variance = 0. The correct population variance is __________.

Mean = 4; Deviations = -2, -1, 3; Squares = 4, 1, 9; Variance = 14 ÷ 3 = 4.67.

Explanation

Mean = 4; Deviations = -2, -1, 3; Squares = 4, 1, 9; Variance = 14 ÷ 3 = 4.67.

Submit

20) For data {1, 2, 3, 6}, the population variance is __________.

Mean = 3; Deviations = -2, -1, 0, 3; Squares = 4, 1, 0, 9; Variance = (4 + 1 + 0 + 9) ÷ 4 = 3.50.

Explanation

Mean = 3; Deviations = -2, -1, 0, 3; Squares = 4, 1, 0, 9; Variance = (4 + 1 + 0 + 9) ÷ 4 = 3.50.

Submit

Variance Calculation Quiz: Calculating Variance (Basic Level)

1) What is the first step to find the variance of a data set?

2)

What first name or nickname would you like us to use?

2) After finding the mean, what should you do next?

3) Why do we square each deviation?

4) Variance can be negative.

5) Find the population variance for data {5, 7, 9, 11}.

6) If all values are equal, what is the variance?

7) Select all correct steps for calculating population variance.

8) Which mistake leads to variance = 0 when it shouldn’t?

9) Find the sample variance for {4, 7, 9}. Round to 2 decimals.

10) For a sample, variance is calculated by dividing by n − 1.

11) Two classes have test scores: A: {70,72,73,75} B: {60,70,80,90}. Which class has the higher variance?

12) Which statements about variance are true?

13) Find the population variance for {0, 2, 4, 6}.

14) Find the sample variance for {10, 12, 15}. Round to 2 decimals.

15) Which of the following are correct steps to find sample variance?

16) Variance is the __________ of the squared deviations.

17) Find the population variance for {3, 4, 5}.

18) For data {8, 10, 12}, the population variance is __________ (round to 2 decimals).

19) For data {2, 3, 7}, a student added deviations to get 0 and said variance = 0. The correct population variance is __________.

20) For data {1, 2, 3, 6}, the population variance is __________.